Solve {l}{(x^2-x)+3}{x+(x^2-4)}

$$\left. \begin{array} { l } { ( x ^ { 2 } - x ) + 3 } \\ { x + ( x ^ { 2 } - 4 ) } \end{array} \right.$$

Least Common Multiple

$$\frac{\left(x^{2}-x+3\right)\left(\left(2x+1\right)^{2}-17\right)}{4}$$

Solution Steps

Factor the expressions that are not already factored.

$$x+x^{2}-4=\left(x-\left(-\frac{1}{2}\sqrt{17}-\frac{1}{2}\right)\right)\left(x-\left(\frac{1}{2}\sqrt{17}-\frac{1}{2}\right)\right)$$

Identify all the factors and their highest power in all expressions. Multiply the highest powers of these factors to get the least common multiple.

$$\left(x-\frac{-\sqrt{17}-1}{2}\right)\left(x-\frac{\sqrt{17}-1}{2}\right)\left(x^{2}-x+3\right)$$

Expand the expression.

$$x^{4}-2x^{2}+7x-12$$

Evaluate

$$x^{2}-x+3,\ x^{2}+x-4$$